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Mechanics of two filaments in tight orthogonal contact [Engineering]
Proceedings of the National Academy of Sciences of the United States of America ( IF 9.412 ) Pub Date : 2021-04-13 , DOI: 10.1073/pnas.2021684118
Paul Grandgeorge, Changyeob Baek, Harmeet Singh, Paul Johanns, Tomohiko G. Sano, Alastair Flynn, John H. Maddocks, Pedro M. Reis

Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple, yet canonical, problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (μCT) and mechanical testing experiments are in excellent agreement with finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibit strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact-pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the μCT and FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small, but nonzero, tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.



中文翻译:

紧密正交接触中的两根长丝的力学[工程]

柔性长丝网络经常涉及紧密接触的区域。由于拓扑结构,几何形状,大的非线性变形和摩擦之间的复杂耦合,因此预测性地了解这些系统的平衡构型具有挑战性。在这里,我们对一个简单但规范的问题进行了深入研究,该问题抓住了细丝之间接触的本质。在正交扣中,使两条细丝接触,每条中心线都位于一对正交平面之一中。我们的X射线断层扫描(μCT)和机械测试实验数据与有限元方法(FEM)模拟非常吻合。尽管物理系统看起来很简单,但即使接触是无摩擦的,数据也表现出惊人的直觉行为。具体来说,我们在两条细丝之间的接触压力场中观察到一条曲线形的菱形脊,有时带有一个内部间隙。当在长丝之间施加相对位移时,就会激活摩擦,并且会形成高度不对称的压力场。这些发现与缠绕在刚体上的单根细丝的经典绞盘分析形成对比。μCT和FEM数据均表明,细丝的横截面会明显变形。但是,理想的几何理论假设管截面不可变形,而忽略了弹性,从质上使我们的观察合理化,并突出了细小但非零的管半径的中心作用。

更新日期:2021-04-06
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